Accurate estimation of the elastic modulus (E) of rock is critical for the design of geotechnical projects such as mining, slopes, and tunnels. However, the determination of rock mechanical parameters usually involves high budget and time requirements. To address this problem, numerous researchers have developed machine learning models to estimate the E of rock. In this study, two novel hybrid ensemble learning models were developed to estimate the E of rock by optimizing the extreme gradient boosting (XGBoost) and random forest (RF) algorithms through the dwarf mongoose optimization (DMO) approach. Firstly, 90 rock samples with porosity, dry density, P-wave velocity, slake durability, and water absorption as input indicators were collected. Subsequently, the hyperparameters of XGBoost and RF were tuned by DMO. Based on the optimal hyperparameters configuration, two novel hybrid ensemble learning models were constructed using the training set (80% of the data). Finally, the performance of the developed models was evaluated by the coefficient of determination (R² score), root mean squared error (RMSE), mean absolute error (MAE), and variance accounted for (VAF) on the test set (20% of the data). The results show that the DMO-RF model achieved the best comprehensive performance with an R² score of 0.967, RMSE of 0.541, MAE of 0.447, and VAF of 0.969 on the test set. The dry density and slake durability were more influential indicators than others. Moreover, the convergence curves suggested that the DMO-RF model can reduce the generalization error and avoid overfitting. The developed models can be regarded as viable and useful tools in estimating the E of rock.

Elastic wave tomography is a non-destructive technique used to obtain velocity images of internal structures. Wave velocity tomography has been used to quantitatively describe abnormal structures and identify boundaries in different media and shapes. This research aims to quantitatively describe anomalous structures on a laboratory scale and identify boundaries in different media and shapes. Wave velocity tomography technology was applied to non-empty and empty anomalous areas, and the accuracy of the resulting velocity images was quantified. The reliability of boundary recognition was studied and analyzed. The accuracy of the results was found to relate to the size and shape of the anomalous structures estimated in the prior model, as well as the wave velocity difference between the anomalous and normal regions. In practical engineering, when the presence of abnormal areas cannot be determined, a completely homogeneous prior model is used. The results indicate that, although the inversion velocity may not be accurate, it is sufficient to identify boundaries. The larger the velocity difference, the clearer the boundary to be recognized. Furthermore, to assess the practical efficacy of this physical detection method, the wave velocity tomography technology was used to detect hidden goafs within a tantalum–niobium mine belonging to the Hunan Fuguihengtong Mining Company. Utilizing physical detection, 12 potential goafs and 100 confirmed goafs were identified within the mine, demonstrating the efficacy of the proposed empty anomalous area detection methodology in accurately identifying and delineating the boundaries of hidden goafs.